probability with combination

There are k sets of numbers : {0,1,2,….,m1}, {0,1,2,……..,m2}, …………,{0,1,2,………,mk}
Such that m1<m2<………<mk.1. How many combinations of k elements can be made taken 1 element from each set such that each set has all distinct elements (no two elements are equal) ?2. What is the probability that any two sets will have at least one element common ?
(Please provide procedure and explanation)

I think the answer given by Plato is the number of permutations, but I am looking for the number of combinations i.e., the sets with all elements same (although in different order) will be treated as one.

AND Plz mention the rule/formula name with explanation so that I can learn them

Re: probability with combination

Originally Posted by achal

There are k sets of numbers : {0,1,2,….,m1}, {0,1,2,……..,m2}, …………,{0,1,2,………,mk}
Such that m1<m2<………<mk.1. How many combinations of k elements can be made taken 1 element from each set such that each set has all distinct elements (no two elements are equal) ?

I for one find this question hard to follow.
Here is the way I read it.
There is a increasing sequence of integers: .
There are sets .
We pick a number from , then we pick a different number from , etc until we pick yet a different number from . Thus we have different selections.

The question seems to be, "How many different selections are possible?"

Note the the number of integers in each set is
If this is the correct setup, the answer is: